Find the extreme points of the function $g(x):=(x^4-2x^2+2)^{1/2}, x∈[-0.5,2]$

I need to find the extreme points of the function $$g(x):=(x^4-2x^2+2)^{1/2}, x∈[-0.5,2]$$
I first found $$f'(x)=\frac{{4x^3-4x}}{2\sqrt {x^4-2x^2+2}}$$ and made $f'(x)=0$ to find all the roots of the function, $x_1=0, x_2=1, x_3=-1$ but since $x_3$ is out of the domain I didn't consider it. Now I have $4$ candidates for the extreme points for this function, namely $x_1, x_2, r_1=-0.5, r_2=2$, where $r_1, r_2$ are the ends of the domain. I then put these candidates back into $f(x)$ and found that $$f(x_2)<f(r_1)<f(x_1)<f(r_2)$$ showing that $x_2$ is the global minimum and $r_2$ is the global maximum.

But I can't seem to figure out the local maximum and local minimum of the function. I tried making a sign table for the function:

But I have no idea how to determine that $x_1$ is the local maximum and $r_1$ is the local minimum.

PS - Sorry for the terrible sign graph, I had to use an online graphing tool.